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Average precipitation by isohyetal method

Short answer

Using the isohyetal method, each interval's mean depth is averaged and weighted by area. Summing area–weighted depths (4443.5 cm·km²) and dividing by total area (600 km²) yields an average precipitation depth of 7.41 cm.

Estimate the average depth of precipitation over the drainage basin with the following data.

Isohyetals (intervals, cm)15-1212-99-66-33-1
Inter-isohyetal area (km2^2)9212812017585

In the isohyetal method the mean depth between two isohyets is taken as the average of their values, and the weighted average is found with the inter-isohyetal areas.

Pˉ=∑AiPˉi∑Ai\bar P = \frac{\sum A_i \bar P_i}{\sum A_i}

For the last band (3-1 cm) the mean is (3+1)/2=2(3+1)/2 = 2 cm.

Isohyetal range (cm)Mean depth PiP_i (cm)Area AiA_i (km²)AiPiA_iP_i
15-1213.5921242
12-910.51281344
9-67.5120900
6-34.5175787.5
3-12.085170
Total6004443.5
Pˉ=4443.5600=7.41 cm\bar P = \frac{4443.5}{600} = 7.41\ \text{cm}

Answer: Average depth of precipitation = 7.41 cm (about 74 mm).

✓ Answer checked by Claude Sonnet 5.5

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